In [ ]:
#importing the necessary libraries
import numpy as np
from lib import *
import pandas as pd
import pennylane as qml
from lib.cr2dataset import hartree, get_pot_cr2
from lib.cr2dataset import cr2_params
from lib.qpe import QPE
import jax
from jax import random
from lib.phase_estimation import *
import phayes
import jax.numpy as jnp
import random as r
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.interpolate import make_interp_spline
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
/var/folders/k9/jxn4k2_s1v50xzyqggp1kft40000gn/T/ipykernel_58085/2955796516.py:4: DeprecationWarning:
Pyarrow will become a required dependency of pandas in the next major release of pandas (pandas 3.0),
(to allow more performant data types, such as the Arrow string type, and better interoperability with other libraries)
but was not found to be installed on your system.
If this would cause problems for you,
please provide us feedback at https://github.com/pandas-dev/pandas/issues/54466
import pandas as pd
In [ ]:
# Set the Seaborn theme and color palette
sns.set_theme(context='paper', style='whitegrid')
dark_palette = sns.color_palette("dark", n_colors=7) # Using a darker palette
# Initialize DataFrame to store the potential data
data_32 = pd.DataFrame()
data_1000 = pd.DataFrame()
states = [1, 3, 5, 7, 9, 11, 13]
labels = ['${}^1\Sigma_g^+$', '${}^3\Sigma_u^+$', '${}^5\Sigma_g^+$', '${}^7\Sigma_u^+$',
'${}^9\Sigma_g^+$', '${}^{11}\Sigma_u^+$', '${}^{13}\Sigma_g^+$']
# Fetch potential data for each state and accumulate it in the DataFrames
for i, state in enumerate(states):
pot, lims = get_pot_cr2(state)
rs_1000 = np.linspace(lims[0], lims[1], 1000)
rs_32 = np.linspace(start=lims[0], stop=lims[1], num=256)
potentials_32 = pot(rs_32) * hartree
potentials_1000 = pot(rs_1000) * hartree
temp_df_32 = pd.DataFrame({'r (a.u.)': rs_32, 'V (cm^-1)': potentials_32, 'State': labels[i]})
temp_df_1000 = pd.DataFrame({'r (a.u.)': rs_1000, 'V (cm^-1)': potentials_1000, 'State': labels[i]})
data_32 = pd.concat([data_32, temp_df_32], ignore_index=True)
data_1000 = pd.concat([data_1000, temp_df_1000], ignore_index=True)
plt.figure(figsize=(12, 8))
sns.lineplot(
data=data_1000,
x='r (a.u.)',
y='V (cm^-1)',
hue='State',
palette=dark_palette,
legend=None
)
sns.scatterplot(
data=data_32,
x='r (a.u.)',
y='V (cm^-1)',
hue='State',
palette=dark_palette,
s=72, # Adjust the size of the scatter plot markers
edgecolor="w",
legend='full'
)
# Configure plot aesthetics
plt.ylim((-17500, 1000))
plt.xlim((2, 8))
plt.xlabel(r'$r$ (a.u.)')
plt.ylabel(r'$V$ (Potential Energy) (cm$^{-1}$)')
plt.title('Potential Energy Curves for Different Electronic States')
plt.legend(title='Electronic State', loc='lower right')
# Display the plot
plt.show()
1.2: Generating the Hamiltonians for all Spin States¶
In [ ]:
mol_params = cr2_params
list_of_spins = [1, 3, 5, 7, 9, 11, 13]
list_of_params32 = [[2.8, 4], [3.2, 4.5], [4, 6.5], [4.3, 6.8], [4.5, 7], [4.6, 7], [5.2, 9]]
hamiltonians = create_hamiltonians(list_of_spins, list_of_params32, mol_params=mol_params)
for i, spin in enumerate(list_of_spins):
params = list_of_params32[i]
variable_name = f"h_dvr_{spin}"
decomposed_hamiltonian = qml.pauli_decompose(hamiltonians[(spin, tuple(params))])
globals()[variable_name] = decomposed_hamiltonian
1.3 Conversion of the hamiltonians into a unitary matrix¶
In [ ]:
wire_order = [0, 1, 2, 3, 4]
n = 5
for spin in list_of_spins:
variable_name = f"ufss{spin}"
hamiltonian = globals()[f"h_dvr_{spin}"]
unitary = convert_to_unitary(hamiltonian, n, wire_order)
globals()[variable_name] = unitary
1.4 Find the true phases of the unitary matrices¶
In [ ]:
for spin in list_of_spins:
unitary_matrix = globals()[f"ufss{spin}"]
phase = find_true_phases(unitary_matrix)
phase = phase/np.linalg.norm(phase)
phase = np.abs(phase/(2*np.pi))
globals()[f"phase{spin}"] = phase
In [ ]:
for spin in list_of_spins:
phase = globals()[f"phase{spin}"]
print(phase.shape)
print(f"True phases for spin state {spin}: {phase}")
(32,) True phases for spin state 1: [0.04096298 0.04450851 0.03373529 0.03641698 0.04883094 0.04707422 0.04618917 0.04335729 0.04236002 0.04286075 0.03153212 0.02933257 0.02824815 0.02153788 0.02175125 0.0180878 0.01859339 0.0256471 0.0104862 0.00672655 0.00572107 0.00376777 0.00121464 0.00027203 0.02241888 0.02029003 0.01805162 0.01533049 0.01363865 0.00616677 0.00840116 0.00825458] (32,) True phases for spin state 3: [0.02901343 0.02373451 0.03744477 0.04043268 0.0427488 0.04435596 0.04636712 0.04968681 0.04959865 0.04161587 0.04204605 0.03526964 0.03264829 0.01655096 0.01354258 0.01365763 0.01005915 0.02640197 0.00565433 0.00484661 0.00216334 0.02348992 0.02325409 0.02170404 0.02199635 0.01558653 0.01279555 0.00834406 0.0092766 0.00902679 0.00247604 0.00232195] (32,) True phases for spin state 5: [0.01227631 0.00621999 0.00261552 0.00198135 0.00339383 0.00250196 0.00124663 0.00148712 0.02469586 0.02625868 0.02744886 0.01272442 0.01362003 0.01481766 0.0317335 0.02972174 0.02082199 0.02099297 0.02160365 0.02358665 0.02330392 0.03152144 0.03432793 0.03763654 0.03866702 0.03931646 0.0414154 0.0411701 0.04617502 0.04629184 0.04383206 0.04384084] (32,) True phases for spin state 7: [0.03247615 0.04127042 0.04582127 0.04682656 0.04935615 0.04803262 0.04830488 0.04015521 0.03836336 0.03455383 0.02986265 0.02907656 0.02588974 0.02264514 0.01966771 0.02723006 0.02580416 0.02644467 0.01410045 0.01252247 0.00749492 0.00653779 0.00323278 0.00115246 0.01668291 0.01541079 0.01466869 0.00436287 0.00975986 0.00909482 0.00761252 0.0077013 ] (32,) True phases for spin state 9: [0.03644479 0.03410099 0.03235278 0.02972791 0.02487595 0.02248715 0.02213779 0.01563024 0.04440149 0.04709256 0.04630769 0.04367538 0.04300372 0.04214087 0.03814891 0.03733337 0.03145188 0.03176127 0.03271724 0.01129369 0.0081831 0.01781276 0.01595272 0.01556459 0.00298519 0.00221959 0.00064878 0.00018968 0.00709408 0.00770577 0.00807828 0.00825916] (32,) True phases for spin state 11: [0.02388759 0.02166877 0.02048656 0.01556992 0.01169694 0.00879841 0.00615253 0.00500117 0.00131725 0.00297208 0.00586808 0.00400173 0.00446676 0.01710126 0.02665297 0.02037801 0.02125365 0.02352124 0.02249257 0.03355426 0.03469166 0.03594763 0.04107166 0.04480059 0.04601715 0.04757934 0.04908886 0.03792824 0.0332597 0.0341589 0.03558577 0.035445 ] (32,) True phases for spin state 13: [0.02667305 0.02834227 0.03292579 0.03407857 0.03630076 0.03544317 0.04465175 0.04655567 0.04831635 0.01516329 0.01289853 0.01196757 0.00946927 0.04294896 0.03566375 0.03503588 0.03888334 0.03964266 0.03955065 0.02637651 0.02455309 0.02127476 0.02116977 0.01578449 0.01294445 0.00698745 0.01036515 0.00980925 0.00114507 0.00114902 0.00204674 0.00204323]
Part 2 Quantum Circuit Generation for Phase Estimation in the Fourier Basis¶
2.1 Obtaining Prior Distribution and Setting Up for Bayesian Estimation¶
In [ ]:
unitaries = [ufss1, ufss3, ufss5, ufss7, ufss9, ufss11, ufss13]
J_max = 2000
num_experiments = 100
c = np.random.random_integers(low=7000, high=8000, size=None)
J_values = [c for i in range(num_experiments)]
n_shots_per_experiment = 1/(1-(1/(2**5)))
ks = []
betas = []
/var/folders/k9/jxn4k2_s1v50xzyqggp1kft40000gn/T/ipykernel_58085/2573652648.py:4: DeprecationWarning: This function is deprecated. Please call randint(7000, 8000 + 1) instead c = np.random.random_integers(low=7000, high=8000, size=None)
2.3 Obtaining the Bayesian Estimation¶
In [ ]:
results = []
for i in range(len(unitaries)):
U = unitaries[i]
unitary_results = []
for l in range(len(U)):
# Generate a new seed for each l, ensuring each unitary eigenvalue has a unique seed
eigenvalue_results = []
phase_estimates = []
true_eigvals, true_eigvecs = jnp.linalg.eig(U)
phi_vec = true_eigvecs[:, l]
n_qubits_U = int(np.log2(U.shape[0]))
for j in range(num_experiments):
random_keys = random.split(random.PRNGKey(0), num_experiments)
prior = initial_fourier_state(J_values[j])
k1= np.random.random_integers(low=20, high=8000, size=None)
beta, k, new_state = phase_estimation_iteration(prior, k1, U, phi_vec, n_qubits_U, n_shots_per_experiment)
fourier_basis_probs = new_state/np.linalg.norm(new_state)
print(fourier_basis_probs)
phase = np.log(np.abs(np.arccos(fourier_basis_probs) - k - beta)) - 2*np.pi
nphase = np.mean(phase/ (2*np.pi))
print(f"Unitary {i+1}, Eigenvalue {l}: Experiment {j + 1} of {num_experiments}, k={k}, beta={beta:.2f}, phases={nphase}")
average_phase = np.mean(nphase)
phase_estimates.append(average_phase)
eigenvalue_results.append((k, beta, new_state, fourier_basis_probs, np.mean(phase_estimates)))
unitary_results.append(eigenvalue_results)
results.append(unitary_results)
/var/folders/k9/jxn4k2_s1v50xzyqggp1kft40000gn/T/ipykernel_58085/1136543756.py:15: DeprecationWarning: This function is deprecated. Please call randint(20, 8000 + 1) instead k1= np.random.random_integers(low=20, high=8000, size=None)
[0.09686879 0.16346608 0.06357014 0.13016744 0.15438464 0.07567874 0.05146155 0.12411314 0.16043894 0.01513575 0.0242172 0.09686879 0.10595024 0.16043894 0.18465614 0.17254753 0.01513575 0.18465614 0.09686879 0.15135749 0.11503168 0.08476019 0.09686879 0.18162899 0.09686879 0.18465614 0.17254753 0.10897739 0.0484344 0.06357014 0.12411314 0.1029231 0.07567874 0.16043894 0.16043894 0.0060543 0.16043894 0.10897739 0.1029231 0.17254753 0.0544887 0.11503168 0.05146155 0.18162899 0.15135749 0.11503168 0.00302715 0.06357014 0.18162899 0.16043894 0.12411314 0.08476019 0.00302715 0.08476019 0.12411314 0.16043894 0.13016744 0.16649324 0.18162899 0.10897739 0.13924888 0.17254753 0.09384164 0.08476019] Unitary 1, Eigenvalue 0: Experiment 1 of 100, k=3278, beta=2.38, phases=0.28840234875679016 [0.23592569 0. 0.13698912 0.03044202 0.01141576 0.23973095 0.03424728 0.11796284 0.23592569 0.03044202 0.14079437 0.05327354 0.16743113 0.02283152 0.13698912 0.03424728 0.02283152 0.04946829 0.01522101 0. 0.07991032 0.07991032 0.1788469 0.06849456 0.19787318 0.14079437 0.14079437 0.23973095 0.17504165 0.02663677 0.03424728 0.07991032 0.02283152 0.14079437 0.22831519 0.02283152 0.00380525 0.07610507 0.02283152 0.14079437 0.03805253 0.1293786 0.22831519 0.07610507 0.01902627 0.13698912 0.14079437 0.02283152 0.0646893 0.03424728 0.22831519 0.07991032 0.03044202 0.22831519 0.16743113 0.22450992 0.02283152 0.01522101 0.07610507 0.09132607 0.02283152 0.13698912 0. 0.22831519] Unitary 1, Eigenvalue 0: Experiment 2 of 100, k=1923, beta=2.35, phases=0.20354494452476501 [0.11618296 0.08255105 0.11006806 0.1253553 0.08560849 0.11618296 0.15287231 0.0397468 0.16204464 0.11618296 0.09783828 0.08560849 0.08866594 0.1253553 0.12841274 0.1253553 0.03363191 0.18344678 0.05809148 0.1651021 0.01834468 0.13452764 0.05197659 0.16204464 0.03363191 0.19261912 0.1253553 0.1253553 0.18956167 0.08866594 0.1131255 0.18650422 0.10395318 0.1253553 0.06420637 0.01834468 0.01222978 0.16204464 0.16204464 0.15287231 0.16204464 0.19261912 0.11618296 0.11006806 0.08255105 0.16204464 0.12841274 0.1253553 0.11618296 0.09783828 0.10395318 0.1131255 0.1253553 0.02445957 0.16204464 0.16204464 0.1253553 0.10395318 0.11618296 0.18650422 0.19261912 0.05503403 0.10395318 0.13147019] Unitary 1, Eigenvalue 0: Experiment 3 of 100, k=1437, beta=2.44, phases=0.15721508860588074 [0.01970478 0.17405888 0.16420649 0.00656826 0.07881911 0. 0.14121759 0.0328413 0.0328413 0.17405888 0.08538737 0.08210324 0.1543541 0.06239847 0.1543541 0.03940956 0.06896673 0.08867151 0.16420649 0. 0.01970478 0.1970478 0.11166042 0.12151281 0.20361605 0.05911434 0.17734301 0.17734301 0.08538737 0.08210324 0.12479694 0. 0.20361605 0.16092236 0.04597782 0.17405888 0.13464934 0.11494455 0.17405888 0.1543541 0.16092236 0.03612543 0.0656826 0.08867151 0.01313652 0.16420649 0.16749062 0.17405888 0.1970478 0.00328413 0.17405888 0.13793346 0.02955717 0.13464934 0.1970478 0.0985239 0.03940956 0.00656826 0.1970478 0.08538737 0.07881911 0.07553498 0.1543541 0.1543541 ] Unitary 1, Eigenvalue 0: Experiment 4 of 100, k=3550, beta=2.34, phases=0.3010835349559784 [0.12676066 0.03083367 0.16444626 0.20555784 0.02055578 0.18842801 0.06851928 0.04111157 0.10963085 0.03425964 0.20555784 0.02055578 0.03083367 0.07194524 0.1712982 0.07879717 0.18500206 0.05481542 0.1712982 0.01370386 0.05138946 0.01370386 0.15416837 0.0376856 0.18157609 0.11648277 0.1610203 0.2089838 0.13361259 0.07537121 0.10963085 0.01712982 0.20555784 0.20555784 0.06851928 0.18500206 0.1712982 0.03083367 0.18842801 0.11648277 0.10963085 0.1712982 0.13361259 0.01712982 0.03083367 0.05138946 0.13361259 0.02055578 0.02055578 0.14046451 0.1712982 0.01370386 0.15759434 0.07194524 0.19185399 0.05138946 0.04453753 0.06851928 0.10277892 0.18157609 0.15759434 0.15074241 0.00685193 0.1610203 ] Unitary 1, Eigenvalue 0: Experiment 5 of 100, k=2268, beta=2.32, phases=0.22979508340358734 [0.17969716 0.05763871 0.02034307 0.13901101 0.03051461 0.03051461 0.13222998 0.10171537 0.21021177 0.15596357 0.1932592 0.10510588 0.01356205 0.18647818 0.00678102 0.00678102 0.1932592 0.10510588 0.12544896 0.19664972 0.05763871 0.05763871 0.14918254 0.14240152 0.12205844 0.21360229 0.12883948 0.21360229 0.17969716 0.02034307 0.00678102 0.15596357 0.18308768 0.17291613 0.20004024 0.15596357 0.15596357 0.01017154 0.12883948 0.17969716 0.08815333 0.15935409 0.16952561 0.06441974 0.10171537 0.15596357 0.11866793 0.01356205 0.05763871 0.03051461 0.00678102 0.1356205 0.12205844 0.02034307 0.07120076 0.12544896 0.08815333 0.04407666 0.00678102 0.03390513 0.16952561 0.00678102 0.05763871 0.11527742] Unitary 1, Eigenvalue 0: Experiment 6 of 100, k=1394, beta=2.42, phases=0.15237963199615479 [0.17454337 0.09879813 0.02963944 0.13831738 0.08233177 0.04610579 0.20088953 0.04939906 0.14161065 0.19759625 0.04281252 0.04610579 0.11855775 0.14490393 0.09879813 0.04610579 0.08562505 0.13831738 0. 0.13831738 0.02963944 0.16795681 0.11855775 0.11526448 0.11197121 0.12185103 0.11197121 0.11526448 0.16466354 0.17454337 0.17454337 0.04610579 0.16466354 0.10538467 0.16795681 0.14819719 0.04281252 0.01646635 0.20088953 0.17454337 0.14490393 0.13831738 0.08562505 0.02963944 0.19759625 0.11197121 0.14161065 0.12185103 0.09550486 0.1251443 0.13831738 0.03293271 0.20747606 0.20088953 0.01317308 0.00658654 0.17454337 0.02963944 0.13831738 0.04610579 0.15478374 0.17454337 0. 0.02963944] Unitary 1, Eigenvalue 0: Experiment 7 of 100, k=35, beta=2.32, phases=-0.43027591705322266 [0.04534974 0.20083454 0.12309214 0.03239267 0.15872407 0.19435601 0.19759528 0.16196334 0.0680246 0.07126386 0.13928847 0.0194356 0.16844188 0.0194356 0.0291534 0.1749204 0.18787748 0.1166136 0.0874602 0.07450314 0.10041727 0.15224554 0.03563193 0.16196334 0.097178 0.17168114 0.05506754 0.12309214 0.1263314 0.15224554 0.19435601 0.145767 0.1263314 0.0291534 0.06478534 0.13928847 0.0583068 0.0291534 0.04211047 0.12309214 0. 0.1749204 0.11985287 0.16844188 0.18787748 0.10041727 0.097178 0.12309214 0.11985287 0.10365654 0.13928847 0.1166136 0.13928847 0.13928847 0.19435601 0.03563193 0.17168114 0.17168114 0.11013507 0.04211047 0.12309214 0.01295707 0.0194356 0.1263314 ] Unitary 1, Eigenvalue 0: Experiment 8 of 100, k=2559, beta=2.35, phases=0.2490033209323883
/var/folders/k9/jxn4k2_s1v50xzyqggp1kft40000gn/T/ipykernel_58085/1136543756.py:15: DeprecationWarning: This function is deprecated. Please call randint(20, 8000 + 1) instead k1= np.random.random_integers(low=20, high=8000, size=None)